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Chapter 6: Problem 59

A certain orbital of the hydrogen atom has \(n=4\) and \(l=2 .\) (a) What are the possible values of \(m_{l}\) for this orbital? (b) What are the possible values of \(m_{s}\) for the orbital?

Short Answer

Expert verified
(a) The possible values of \(m_{l}\) for this orbital are \(-2, -1, 0, 1,\) and \(2\). (b) The possible values of \(m_s\) for this orbital are \(+\frac{1}{2}\) and \(-\frac{1}{2}\).

Step by step solution

01

(a) Determine the possible values of \(m_{l}\)

The magnetic quantum number, \(m_l\), can take integer values ranging from \(-l\) to \(+l\). For the given value of \(l=2\), the possible values of \(m_l\) are \(-2, -1, 0, 1,\) and \(2\).
02

(b) Determine the possible values of \(m_{s}\)

The spin quantum number, \(m_s\), can take two possible values for an electron in any orbital. These values are \(+\frac{1}{2}\) and \(-\frac{1}{2}\). Therefore, the possible values of \(m_s\) for the given orbital are \(+\frac{1}{2}\) and \(-\frac{1}{2}\).

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Most popular questions from this chapter

The series of emission lines of the hydrogen atom for which \(n_{1}=3\) is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed. (b) Calculate the wavelengths of the first three lines in the Paschen series - those for which \(n_{1}=4,5,\) and \(6 .\)

Write the condensed electron configurations for the following atoms and indicate how many unpaired electrons each has: (a) \(\mathrm{Mg},(\mathbf{b}) \mathrm{Ge},(\mathbf{c}) \mathrm{Br},(\mathbf{d}) \mathrm{V},(\mathbf{e}) \mathrm{Y},(\mathbf{f}) \mathrm{Lu}\)

One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. (a) In what region of the elertromagnetic spectrum is this emission found? (b) Determine the initial and final values of \(n\) associated with this emission.

Write the condensed electron configurations for the following atoms, using the appropriate noble-gas core abbreviations: (a) \(\mathrm{Cs},(\mathbf{b}) \mathrm{Ni},(\mathbf{c}) \mathrm{Se},(\mathbf{d}) \mathrm{Cd},(\mathbf{e}) \mathrm{U},(\mathbf{f}) \mathrm{Pb}\)

List the following types of electromagnetic radiation in order of increasing wavelength: (a) the gamma rays produced by a radioactive nuclide used in medical imaging; (b) radiation from an FM radio station at 93.1 \(\mathrm{MHz}\) on the dial; (c) a radio signal from an AM radio station at 680 \(\mathrm{kHz}\) on the dial; ( d ) the yellow light from sodium vapor streetlights; (e) the red light of a light-emitting diode, such as in a calculator display.
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